The definition of mass in asymptotically de Sitter space-times

TL;DR

This paper introduces an invariant method to define and compute the mass of objects in asymptotically de Sitter space-times using a local sphere, applicable even within the cosmological horizon.

Contribution

It presents a new local definition of mass in de Sitter space that does not depend on asymptotic regions and accommodates perturbations like gravitational waves.

Findings

Mass can be calculated exactly on a sphere inside the cosmological horizon.

The formalism handles perturbations satisfying linearized equations without requiring shared symmetry.

Applicable to stationary space-times with gravitational wave perturbations.

Abstract

An invariant definition of mass in asymptotically de-Sitter space-times is given that relies on the existence of a time-like Killing vector on a sphere surrounding the mass but does not require going to an asymptotic region. In particular the mass can be calculated exactly on a sphere inside the cosmological horizon. The formalism requires varying the background metric solution by a perturbation that satisfies the linearized equations of motion but need not share the Killing symmetry of the solution and is therefore ideally suited to calculating masses in stationary space-times perturbed by a gravitational wave without going beyond the cosmological horizon.